Sept. 28, 1871 | 
NATURE 
425 

my remarks inp. 63. My belief is now, as it has been for years 
(long before Mr. Stone’s paper was published), that under 
favourable conditions an exceedingly fine ligament must be visible 
at the moment of real internal contact, the planet’s outline being 
otherwise undistorted. But in most instances a coarser ligament 
is formed xo¢ contemporaneously with the moment of real con- 
tact. I have shown that the true moment of contact can be 
injerret from the formation of a coarser ligament as exactly as 
when a fine ligament is observed. This I still maintain, and I 
further believe that Mr. Stone’s opinion as to the cause of the 
phenomenon, an opinion independently enunciated by myself in 
November 1868 (see Scvevtific Opinion) is correct, and that the ex- 
perimen al tests which have been supposed to disprove it, have 
in reality no sufficient bearing on the question at issue. 
7. Atp. 63. Itis unfortunate if my account of Stone’s proceed- 
ings suggests that I maintain he was the first to consider whether 
real or apparent contacts had been observed ; for I have but lately 
been maintaining the contrary view in a correspondence with an 
ex-president of the Royal Astronomical Society. I have invariably 
opposed the opinion here ascribed to me. Mr. Stone himself 
has never claimed what I am said to have claimed for him, He 
has made a definite claim, and that claim I have repeated and 
still hold to be just. 
Prof. Newcomb concludes with some general statements. He 
considers I am mistaken in supposing that astronomers generally 
regard observations on Venus in transit as the most trustworthy 
method of obtaining the solar parallax ; mistaken again in sup- 
posing that Mr. Stone has removed any ‘‘difficulties that had 
perplexed astronomers ;” and so on. Such statements are so 
vague that I shall scarcely be expected to discuss them. Until 
proof, or atleast some evidence to the contrary, is supplied, I 
can only say that now, as when I wrote ‘* The Sun,” my opinions 
on these points seem to me to be just. I am certainly not alone 
in holding them. RICHARD A. PROCTOR 
Brighton, September 23 

Elementary Geometry 
f 
THE question raised on this subject naturally consists of two 
parts. The first relates to the unsuitableness of Euclid as a text- 
book, and the need of a work which shall so commend itself to ex- 
aminers and teachers, so to supplant it. The second question is 
—given the authoritative text-book, how is the geometry of which 
it treats to be taught to young students? The arguments on the 
first of these questions have been so ably and conclusively stated 
lately by several mathematicians, especially by Mr. Wilson, Dr. 
Joshua Jones, and Dr, Hirst, that there is no need to revive the 
discussion ; but I entirely agree with your correspondent in his 
conclusion that the book which is to supplant Euclid is at present 
a desideratum, and that it will probably be the work of more 
heads than one. Several books have been written during the 
last four years, and have formed the basis of the discussions 
which have since taken place on the requirements of the new 
programme. By theic means, the questions at issue between the 
Opponents and supporters of Euclid have become more clearly 
defined, and a greater unanimity of action has resulted amongst 
those who are labouring to supply this desideratum of modern 
education. But I am sure that most of these authors will admit 
that the issue of works intended for permanent text-books was 
premature, 
When the first question is settled, the second remains. Geo- 
metry is not essentially difficult, nor is it generally distasteful to 
young students. It becomes so, however, when they are required 
to commit the propositions to memory before they understand 
them, The educational purpose which geometry serves is not 
the discipline and exercise of the memory. A choice and pregnant 
passage from a good author may be learnt and retained in the 
memory without much difficulty, although its meaning may be 
very imperfectly understood, and it will richly repay the labour 
of its acquisition. It will be recalled again and again, and re- 
ceive new light, and afford new pleasure with every fresh associ- 
ation. Not so with geometry; it is useless if not understood, 
A child should be made to comprehend even the definitions 
before he commits them to memory. Let us suppose, for in- 
stance, that the definition of a circle is to be learnt, the 
prelimimary explanation should take some such form as the 
following, 
The teacher at the black-board, with chalk and compasses, and 
the pupils at their desks, with paper and compasses—the teacher 
draws a,circle and names the figure—he tells each boy also to 
make a circle, and then proceeds to question. What name is 



given to such a surface as that on your drawing paper? What 
kind of a figure shall we call one which can be drawn on a 
plane surface? Compare a triangle and a circle, and say how 
many lines form the boundary of the triangle? How many 
Ines contain the circle? Explain exactly what you do with 
the points of the compasses when you use them to make a 
circle? Why must the joint of the compasses be tight? Fix 
a drawing-pin in your drawing-board, and with a piece of 
thread construct a circle. What purpose does the thread 
serve in the construction? The defning properties of a circle 
are, therefore, these—(1) it is a plane figure; (2) it is 
bounded by one line, termed the circumference (3); every 
point of the circumference is at the same distance from a 
fixed point, termed the centre. 
After the definition is worded in its permanent form, and 
repeated, and written several times on paper, it will be re- 
membered. 
Again, let us suppose the propositions on the equality of 
triangles to be the subject; the following introductory ques- 
tions and exercises suggest themselves. Draw two straight 
lines, one 5 in. long, and the other 8 in.; then make with 
your protractor an angle of 43°. Construct a triangle having 
one of its angles equal to the angle drawn, and the sides of 
this angle equal to the given straight lines. Take the figures 
drawn by different boys, and compare them as regards size. 
Now consider the parts of each ; how many sides has each ? How 
many angles ? How many sides are drawn from given dimensions ? 
Letter them and then name them. How many angles? Name it. 
How many angles were not originally given? Name them. How 
many sides? Name it. Compare this third side, B C, in two 
of the figures. If the figures are all accurately drawn through- 
out the class, what must necessarily follow with regard to 
this third side BC in all the figures, &c. ? 
Finally, the proposition should be enunciated, and the 
proof learnt in the form in which it is to be remembered. 
Then the teacher may give three angles which may form 
the angles of a triangle, and when the cons‘ructions are made 
compare two figures from distant parts of the class. Similarly 
he may treat all the allied propositions. When taught in this 
way, the subject becomes so easy and attractive that it may 
be commenced at an early age. 
If, as some teachers maintain, Spartan severity be necessary 
to secure mental discipline, then this plan of teaching elemen- 
tary geometry will not be an improvement on that of forcing 
into the memory Euclid, pure and simple, without note or 
comment ; bat when the test of success is applied, I am sure 
the plan of making the early school work as easy and as 
pleasant as possible will require no other argument to support 
it. R. WORMELL 
“eat 
It is remarkable that Prof. Everett a:serts 4 to represent the 
reduced height of the mercurial column, when the wxreduced 
height is carefully indicated in Fig. 264 by the same symbol 4. 
Moreover it is distinctly stated on page 362 that ‘‘ the tension of 
the vapour is evidently equal to the external pressure minus ¢/e 
height of the mercury inthe tube,” 
Prof. Everett writes, ‘‘ In some instances I have endeavoured 
to simplify the reasonings by which propositions are established 
or formulz deduced” (Preface, part 1). This would lead most 
people to expect simplicity, which includes accuracy ; and they 
may well be astounded when they find not only unexplained but 
inaccurate formule. Prof. Everett’s promises, and not his com- 
plaint, were the grounds of expectations which have not been 
realised. 
Deschanel’s 
THE REVIEWER OF DESCHANEL’S ‘‘HEAT” 
Sept. 22 

Science 
Mr. Forbes does not stand alone in his experience of news- 
paper science. The G/ode, however, is not generally looked on 
as a scientific paper, and no one would be likely to go to it for 
information on matters other than political. What shall we say, 
however, to the following paragraph, copied verbatim et literatim 
from the columns of the Mark Lane Express for September 4 ?— 
Newspaper 
“© CHARLOCK.—A correspondent inquires what he must do to 
abate the annoyance of it in his crops. We do not believe there 
is any mode of preventing its presence. Some seasons are dis- 
tinguished by its appearance. We do not think they come from 
